JUMP DEGREES OF TORSION-FREE ABELIAN GROUPS

被引：6

作者：

Andersen, Brooke M. ^{[1
]}

Kach, Asher M. ^{[2
]}

Melnikov, Alexander G. ^{[3
]}

Solomon, Reed ^{[4
]}

机构：

[1] Assumption Coll, Dept Math & Comp Sci, Worcester, MA 01609 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[3] Univ Auckland, Dept Comp Sci, Auckland 1142, New Zealand

[4] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2012年 / 77卷 / 04期

关键词：

torsion-free abelian group; jump degree; ORDERINGS; SET;

D O I：

10.2178/jsl.7704020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show, for each computable ordinal a and degree a > 0((alpha)), the existence of a torsion-free abelian group with proper alpha th jump degree alpha.

引用

页码：1067 / 1100

页数：34

共 18 条

[1] [Anonymous], 1970, PURE APPL MATH, V36
[2] JUMPS OF ORDERINGS
ASH, CJ
JOCKUSCH, CG
KNIGHT, JF
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 319 (02) : 573 - 599
[3] ASH CJ, 2000, STUDIES LOGIC FDN MA, V144
[4] Every set has a least jump enumeration
Coles, RJ
Downey, RG
Slaman, TA
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 62 : 641 - 649
[5] ORDERINGS WITH ALPHA-TH JUMP DEGREE 0(ALPHA)
DOWNEY, R
KNIGHT, JF
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 114 (02) : 545 - 552
[6] The isomorphism problem for torsion-free Abelian groups is analytic complete
Downey, Rod
Montalban, Antonio
[J]. JOURNAL OF ALGEBRA, 2008, 320 (06) : 2291 - 2300
[7] COUNTABLE ALGEBRA AND SET EXISTENCE AXIOMS
FRIEDMAN, HM
SIMPSON, SG
SMITH, RL
[J]. ANNALS OF PURE AND APPLIED LOGIC, 1983, 25 (02) : 141 - 181
[8] FUCHS L, 1973, PURE APPL MATH, V36
[9] The isomorphism relation on countable torsion free abelian groups
Hjorth, G
[J]. FUNDAMENTA MATHEMATICAE, 2002, 175 (03) : 241 - 257
[10] BOOLEAN-ALGEBRAS, STONE SPACES, AND THE ITERATED TURING JUMP
JOCKUSCH, CG
SOARE, RI
[J]. JOURNAL OF SYMBOLIC LOGIC, 1994, 59 (04) : 1121 - 1138

← 1 2 →